Fibonacci Numbers

Leonardo of Pisa, known as Fibonacci,was a mathematician in the 11th and 12th centuries. A set of numbers, called the Fibonacci numbers ,are named after him. These numbers form a sequence. The first part of the sequence is

1, 1, 2, 3, 5, 8, 13, 21, 34 , 55, ...

notice that

a(1) = 1

a(2) = 1

a(3) = a(1) + a(2) = 1+1 = 2

a(4) = a(2) +a(3) = 1+2 = 3

a(5) = a(3) +a(4) = 2+3 = 5

where a(n) represents the nth term of the sequence.

Each term of the sequence , after the first two, is given by the sum of the previous two.

In general,

a(n) = a(n-2) + a(n-1).

For n > 2.

We can find the next term in the sequence

a(11) = a(9) + a(10) = 34 + 55 = 89

and the next

a(12) = a(10) + a(11) = 55 + 89 = 144

We can find any term of the sequence by following this pattern.

To meet my children and find an application for Fibonacci numbers, please visit Fibonacci and Babies.